\item \subquestionpoints{5} Consider the Poisson distribution parameterized by
$\lambda$:
%
\begin{equation*}
  p(y; \lambda) = \frac{e^{-\lambda}\lambda^y}{y!}.
\end{equation*}
%
Show that the Poisson distribution is in the exponential family, and
clearly state the values for $b(y)$, $\eta$, $T(y)$, and $a(\eta)$.

\ifnum\solutions=1{
  \input{03-poisson/01-exponential-sol}
}\fi
